Diffractive optical element and also optical arrangement comprising a diffractive optical element

ABSTRACT

A diffractive optical element has a plurality of diffraction structures for a certain wavelength. These each have a width measured in the plane of the diffractive optical element and a height measured perpendicularly thereto. The widths and the heights of the diffraction structures vary over the area of the diffractive optical element. An optical arrangement comprising such a diffractive optical element has, in addition, a neutral filter. The efficiency of such a diffractive optical element and of such an arrangement can be optimized locally for usable light.

This application is a continuation of U.S. application Ser. No.10/818,614, filed in the United States on Apr. 6, 2004, which is acontinuation of U.S. application Ser. No. 10/144,452, filed in theUnited States on May 10, 2002, now U.S. Pat. No. 6,728,036, which claimspriority to German Patent Application No. 101 23 230.6 having a filingdate of May 12, 2001.

BACKGROUND OF THE INVENTION

The invention relates to a diffractive optical element and also anoptical arrangement comprising a diffractive optical element.

A diffractive optical element is disclosed in the specialist paper“Zonal diffraction efficiencies and imaging of micro-Fresnel lenses” inJ. Mod. Opt., 45, 1405, 1998. The latter proposes reducing thestructural heights of the diffraction structures with increasing radiusof the Fresnel lenses therein, that is to say with decreasing structuralwidth, and this, in the case of the optical boundary conditions chosentherein, results in an increase in the diffraction efficiency at thelens rim.

In the case of many diffractive optical elements in which, as is stillbeing discussed, the diffraction efficiency decreases with smallerstructural width, such a variation in the structural height does not,however, result in an improvement in the diffraction efficiency, withthe result that the teaching of the specialist paper cannot begeneralized. A diffractive optical element having constant structuralheights is disclosed in U.S. Pat. No. 5,623,365 A. One of thetransmissive diffractive optical elements described therein has thefunction of a lens having a certain focal length. This necessitates thatthe widths of the diffraction structures become smaller with increasingdistance from the central point. The greater the desired refractingpower of such a diffractive optical element with a given refractiveindex is to be, the greater becomes the variation in the widths of thediffractive structures with the distance from the central point and,consequently, the variation in the ratio of said widths and of thewavelength, which ratio is mainly responsible for the achievable localdiffraction efficiency.

In the case of a diffractive optical element according to the type ofU.S. Pat. No. 5,623,365 A, said variation in the ratio of structuralwidth and wavelength manifests itself, as calculations based on theelectromagnetic diffraction theory have shown, in that the more light isdiffracted into other orders of diffraction, the narrower are thediffraction structures. This results in losses in the local diffractionefficiency in the region of narrower diffraction structures, and thisresults in a variation, usually undesirable, in the local diffractionefficiency of the diffractive optical element.

EP 0 312 341 A2 describes a transmissive diffractive optical elementthat has a plurality of concentrically disposed diffraction regions thatare each designed for different illumination wavelengths and withinwhich there is a constant structural height. Within each of saiddiffraction regions, therefore, the disadvantages explained inconnection with U.S. Pat. No. 5,623,365 A also occur here in the case ofa variation of the structural widths, and this affects the dependence ofthe local diffraction efficiency.

The diffractive optical element in EP 0 312 341 A2 may, in addition,have annular zones that are of opaque or partially transparent design inorder to modify the light passing through so as to achieve a desiredintensity distribution in the beam path downstream of the diffractiveoptical element. EP 0 312 341 A2 consequently discloses an opticalarrangement wherein the constant structural heights of the diffractionstructures for an illumination wavelength also result in thedisadvantages that were discussed in connection with U.S. Pat. No.5,623,365 A.

It is therefore a first object of the present invention to develop adiffractive optical element in such a way that its local diffractionefficiency is optimally adapted to the application purpose.

Said object is achieved, according to the invention, by a diffractiveoptical element having the features of the present invention.

SUMMARY OF THE INVENTION

Diffractive optical elements are used, for example, to correct forcertain aberrations in an optical arrangement, for example thelongitudinal color aberration, the color magnification error, thesecondary spectrum and also the color variation in the coma. Inaddition, monochromatic aberrations may also be corrected.

The invention is based on the insight that the height of the diffractionstructures can be used as a degree of freedom to modify the localdiffraction efficiency of the diffractive optical element and can bealtered over the area of the diffractive optical element. At the sametime, it was recognized that the teaching of the specialist paperrelating to reducing the structural heights so as to increase thediffraction efficiencies of less wide diffraction structures is achievedonly in the case of special optical boundary conditions in which animprovement in the blaze effect is achieved by reducing the structuralheights and actually results in an increase in the diffractionefficiency. In most other cases, in which the blaze effect is notimproved in this way by the structural height change, the teaching ofthe specialist paper achieves precisely the opposite of the desiredeffect, namely a reduction in the diffraction efficiency at those pointsat which it should actually be increased according to the specialistpaper, namely in the region of low diffraction structures.

The diffractive optical element according to the invention increases thecomparatively low diffraction losses in the region of the widestructures and, thus, matches them to the comparatively largediffraction losses in the region of the less wide structures in such away that a diffractive optical element results that has a localdiffraction efficiency remaining constant over its area, and this isdesirable for many application cases. In addition, required patterns oflocal diffraction efficiencies can be achieved by means of thestructural height variation without substantial impairments having to beaccepted in other imaging properties of the diffractive optical elementin the process.

Because of the structural height variation in the region of the lesswide diffraction structures, the diffractive optical element accordingto the invention has lower efficiency losses due to structural heightthan in the region of the wider diffraction structures. This is utilizedto compensate completely or partly or even to overcompensate for themagnitude of the diffraction efficiency due to structural width in theregion of the less wide diffraction structures that inevitably occur inthe case of diffractive optical elements having constant structuralheight. In the case of overcompensation, the diffractive optical elementhas the highest diffraction efficiency at those points where, normally,the diffraction efficiency is lowest, namely in the region of thediffraction structures having the smallest widths.

In a preferred embodiment of the invention, a diffractive opticalelement in accordance with claim 2 has the constant pattern,particularly desired for many application cases, of the diffractionefficiency function over the area of the diffractive optical element.Said pattern is achieved by compensating exactly for the increase in thediffraction efficiency in the case of larger structural widths by acorresponding reduction in the structural height in the region of widediffraction structures. In this connection, preferably proceeding froman optimum structural height for the diffraction structure, for whichknown calculating formulae exist, the structural height is reduced.

The diffractive optical element in accordance with claim 3 makes itpossible to fulfill, for example, requirements relating to thediffraction efficiency function of the diffractive optical element, inwhich the diffraction efficiency function should increase towards therim of the diffractive optical element. Such a diffractive opticalelement is able, for example, to compensate for a radially oppositelydirected diffraction efficiency decrease of other optical components.

The diffractive optical element in accordance with claim 4 may be usedas an apodization element.

A diffractive optical element in accordance with claim 5 can be producedwith acceptable cost and is not very alignment-critical because of itsrotational symmetry.

The diffraction efficiency is increased in the case of a diffractiveoptical element in accordance with claim 6.

The diffractive optical element can be designed as a transmissivediffractive optical element in accordance with claim 7 or as areflective optical element, depending on application purpose.

A further object of the present invention is to develop an opticalarrangement comprising a diffractive optical element according to thepreamble of claim 9 in such a way that its flexibility is increased yetagain if the required local total efficiencies are implemented for theoptical arrangement.

This object is achieved, according to the invention, by an opticalarrangement having the features of claim 9.

An additional neutral filter makes it possible to implement, forexample, fine adjustments to achieve a required total efficiencyfunction. The local total efficiency of the optical arrangement is madeup in this connection of the local diffraction efficiency of thediffractive optical element and, optionally, further diffractive opticalcomponents and the local transmission of the neutral filter and,optionally, of further optical components. The transmission function ofthe neutral filter may, in this connection, be stepless, i.e. have acontinuous transmission pattern or, alternatively, be graded, i.e. havediscrete changes in the transmission.

Since neutral filters are, as a rule, less critical in the alignment ofan optical arrangement, an optical arrangement can be realized in whicha plurality of neutral filter shaving various transmission functions canbe substituted for one another in order, in this way, to achievedifferent required total efficiency functions. Desired local effectsthat could be achieved only at higher cost by means of the variation inthe structural height of the diffractive optical element can also beproduced in such an optical arrangement with the aid of the neutralfilter.

An optical arrangement in accordance with claim 10 is an apodizationelement that can be used for a number of application cases.

An optical arrangement in accordance with claim 11 has a reduced numberof optical interfaces.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments of the invention are explained in greater detailbelow by reference to the drawings; in the drawings:

FIG. 1 shows a meridional section through a diffractive converging lensaccording to the prior art;

FIG. 2 shows a detail of FIG. 1;

FIG. 3 shows a detail, similar to FIG. 2, of a diffractive converginglens according to the invention;

FIG. 4 shows a detail, similar to FIG. 2, of a further diffractiveconverging lens according to the prior art;

FIGS. 5 to 7 show schematic diagrams of the local diffractionefficiencies of the converging lenses according to FIGS. 2 to 4 as afunction of the distance from the central point;

FIG. 8 shows a diagram with calculated structural heights of adiffractive converging lens similar to FIG. 3;

FIG. 9 shows a diagram with calculated local diffraction efficiencypatterns of the diffractive converging lens having structural heights inaccordance with FIG. 8 as a function of the distance from the centralpoint;

FIG. 10 shows a diagram with calculated local phase patterns of thediffractive converging lens having structural heights in accordance withFIG. 8 as a function of the distance from the central point;

FIG. 11 shows a diagram with calculated structural widths of adiffractive converging lens similar to FIG. 3;

FIG. 12 shows an optical arrangement according to the inventioncomprising a diffractive converging lens in accordance with FIG. 4; and

FIG. 13 shows a schematic diagram with the local diffraction efficiencypattern of the optical arrangement in accordance with FIG. 12.

DETAILED DESCRIPTION OF THE INVENTION

The diffractive converging lens denoted in total in FIG. 1 by thereference symbol 1 corresponds to the prior art. On one side, it has aplurality of diffraction structures 2 to 9 that are disposedrotationally symmetrically with respect to the optical axis 10 of thediffractive converging lens 1. On the other side, the diffractiveconverging lens 1 has a flatly terminating counter surface 11.

The central diffraction structure 2 has a convex surface. Its radialtermination forms a cylindrical step surface 12 that is part of thediffraction structure 3 and surrounds the diffraction structure 2annularly. Adjacent to the step surface 12 is a diffraction surface 13that slopes radially outwards and that is likewise part of thediffraction structure 3. The diffraction structures 4 to 9 likewisehave, like the diffraction structure 3, a step surface and a diffractionsurface that alternate radially from the inside outwards in thediffractive converging lens 1. In the meridional section of FIG. 1, thisresults in a structure, sawtooth-shaped in total, of that surface of thediffractive converging lens 1 situated opposite the counter surface 11.

The diffraction surfaces of the diffraction structures 2 to 9 (cf.diffraction surface 13) slope outwards at an angle that is such that thelight is preferentially guided into a certain order of diffraction forwhich the diffraction condition is fulfilled because of the widths ofthe diffraction structures 2 to 9. Such an adapted shape of thediffraction structures is denoted as a “blaze profile”.

The height h of the diffraction structures 2 to 9, i.e. their extensionin the direction of the optical axis 10 from the respective highestpoint to the respective lowest point of the diffraction structure 2 to9, is equal for all the diffraction structures 2 to 9. For thediffraction structures 3 to 9, the height h corresponds to the extensionof the step surfaces (cf. step surface 12 of the diffraction structure3) parallel to the optical axis 10.

The width of the diffraction structures 2 to 9, i.e. the radialextension with respect to the optical axis 10, varies over thediffraction structures 2 to 9 in accordance with a required phasefunction and decreases continuously from the diffraction structure 2 tothe diffraction structure 9. The width r 7 of the diffraction structure7 is shown as representative in FIG. 1. The width of a diffractionstructure at a certain distance from the central point is in this case ameasure of the phase function achieved in the diffractive converginglens 1.

The heights h and also the widths r are of a size that is comparablewith the wavelength of the light for which the diffractive converginglens 1 is to be used. The ratio of the width r and the wavelength usedis in this case in the range between 1 and >100.

The rim region of the diffractive converging lens 1 is magnified yetagain in the detail shown in FIG. 2.

The radial pattern of the diffraction efficiency T can be calculated onthe basis of the electromagnetic diffraction theory for a diffractiveconverging lens 1 in accordance with FIGS. 1 and 2 having constantheight of the diffraction structures.

The result of such a calculation is shown diagrammatically in FIG. 5.Proceeding from a diffraction efficiency value T0, i.e. the diffractionefficiency of the diffraction structure 4, the diffraction efficiency Tdecreases towards the outermost diffraction structure 9 to a rim valueTR. The diffraction efficiency T therefore decreases with respect to thedistance R from the central point with decreasing width r of thediffraction structures 4 to 9.

Further embodiments of diffractive converging lenses are discussedbelow. Components that correspond in this connection to those that havealready been described above with reference to the drawing are givenreference symbols increased by 100 in each case and are not explained indetail yet again.

The detail diagram of FIG. 3, which is similar to that of FIG. 2, showsa diffractive converging lens 101 according to the invention. Thediffraction structures 104 to 109 have the same sawtooth-type basicshape as the corresponding diffraction structures 4 to 9 of thediffractive converging lens 1. The widths r of the diffractionstructures 104 to 109 are also equal to those of the diffractionstructures 4 to 9 as, for example, a comparison of the widths r7 of thediffraction structure 7 and r107 of the diffraction structure 107 shows.

Those portions of the diffraction structures 104 to 109 extendingfurthest away from the counter surface 111, that is to say the tips ofthe sawteeth, are at the same distance from the counter surface 111 forall the diffraction structures 104 to 109, as is the case for thediffractive converging lens 1 according to the prior art. In the case ofthe diffractive converging lens 101 according to the invention in FIG.3, however, the height of the step surfaces 114 to 118 of thediffraction structures 105 to 109 decreases with decreasing distancefrom the central point and, therefore, with increasing width of thediffraction structure. The height of the diffraction structure 105,h105, is therefore less than the height of the diffraction structure109, h109.

The blaze profile of the diffraction structures of the diffractiveconverging lenses 101 may be designed as a continuously inclined surfaceor, alternatively, by means of a known multilevel structure having astaircase-type pattern.

FIG. 6 shows diagrammatically the pattern of the local diffractionefficiency of the diffraction structure 101 as a function of thedistance from the central point. The diffraction efficiency T isconstant between the diffraction structures 104 and 109 and equal to therim value of the diffraction efficiency of the diffraction structure109, TR. This is due to the fact that two effects modifying thediffraction efficiency compensate in the case of the diffractiveconverging lens 101: on the one hand, the diffraction efficiencyincreases with increasing width r of the diffraction structures 109 to104, as already discussed in relation to the diffractive converging lens1 (cf. FIG. 5). On the other hand, the diffraction efficiency decreaseswith decreasing height of the diffraction structures 109 to 104. In thecase of the diffractive converging lens 101, the height variation isaligned with the width variation in such a way that, in total, aconstant diffraction efficiency TR results with respect to the distanceR from the central point.

The local diffraction efficiency pattern in the case of a diffractiveconverging lens 101 that has diffraction structures with an outwardlydecreasing width and increasing height, was discussed above with the aidof FIGS. 3 and 6. The result of quantitative calculations based onelectromagnetic diffraction theory is shown in FIGS. 8 to 10.

FIG. 8 shows the dependence of the height h, in nm, of the diffractionstructures on the distance R from the central point for a diffractiveconverging lens having a structure that corresponds to the principleaccording to that of FIG. 3. The height of the diffraction structures atthe rim for R=110 mm is h=480 mm. The height h of the diffractionstructures decreases progressively in the direction of the central pointof the diffractive lens down to a height h=429 nm at a distance R=33 mmfrom the central point. Plotted against the distance R from the centralpoint, such a pattern of heights h of the diffraction structures resultsin a diffraction efficiency T that is shown in FIG. 9. Substituted inthe calculation of the diffraction efficiency T as parameters were anillumination wavelength of 248.34 nm and also a refractive index of thematerial of the diffractive converging lens of 1.508. The diffractionstructures have a blaze profile.

For both polarization directions TE (open triangles) and also TM (opencircles), the diffraction efficiency remains approximately constant at adiffraction efficiency value of approximately 0.89. The diffractionefficiency values for the TE polarization tend to be minimally higherthan those for TM polarization. Here, the calculation was againperformed without an anti- reflection coating of the diffractiveconverging lens.

FIG. 10 shows the pattern of the phase P of the light passing throughthe respective diffraction structures in rad against the distance R fromthe central point for a height pattern of the diffraction structures inaccordance with FIG. 8. The curve shape of the phase pattern correspondsqualitatively to that of the height pattern in FIG. 8. Proceeding from arelative value of 0 rad at R=100 mm, the phase P follows progressivelydown to a value of −0.06 rad at R=33 mm.

If a constant phase pattern is desired over the cross-section of theillumination beam for an optical arrangement having such a diffractiveconverging lens, a phase pattern of the type shown in FIG. 10 has to beprecompensated for in other optical components, for example inrefractive optical components.

FIG. 11 shows the pattern of the structural width r of the diffractionstructures of the diffractive converging lens which results in thediffraction efficiencies in accordance with FIG. 9. Proceeding from therim of the converging lens (R=110 mm), the structural width increasesfrom a width of r=2.5 m to a width of r=60 min the region of the centerof the converging lens (r=5 mm).

A further variant of a diffractive converging lens 201 according to theprior art is shown in FIG. 4. In the latter, the pattern of the heightsh of the diffraction structures 204 to 209 is precisely the reverse ofthat for the diffractive converging lens 101 of FIG. 3, i.e. the heightsh decrease from the innermost, widest diffraction structure 204 shown inFIG. 4 to the outermost, narrowest diffraction structure 209. The heightof the diffraction structure 209, h209, is accordingly less than theheight of the diffraction structure 205, h205.

In the diffractive converging lens 201, the two effects that modify thelocal dependence of the diffraction efficiency T enhance one another: onthe one hand, the width r of the diffraction structures and, on theother hand, their height h decrease outwards, and this results in eachcase in a reduction in the diffraction efficiency. The consequence isthe diffraction efficiency pattern that is shown diagrammatically inFIG. 7. In the latter, proceeding from a diffraction efficiency value T0of the diffraction structure 204, the diffraction efficiency T decreasesas a function of the distance R from the central point with a greaterslope than in FIG. 5, thereby resulting in a lowest value of thediffraction efficiency, Tmin, that is lower in the case of thediffractive converging lens 201 than in the case of the diffractiveconverging lens 1.

It is clear that practically any diffraction efficiency patterns can beestablished by means of required variations in the widths r and theheights h of the diffraction structures. In this connection, the widthsr do not have to decrease monotonically from the inside outwards, asdescribed above, but may also increase monotonically or even have otherdependencies that can be described, for example, by exponentialfunctions of the distance R from the central point and may have main andsubsidiary maxima or minima.

The diffractive converging lenses 1 to 201 may have an anti-reflectioncoating to increase their diffraction efficiency.

An additional degree of freedom for setting a desired radial totalefficiency pattern for usable light into which both the diffractionefficiencies and the transmissions of the optical elements involvedenter results from the use of a neutral filter 220. FIG. 12 shows anoptical arrangement according to the invention that is exemplary forthis purpose and that shows the combination of the neutral filter 220with a diffractive optical element in accordance with FIG. 4. Theneutral filter 220 is joined to the counter surface 211 of thediffractive converging lens 201. This joint can either be made by meansof a suitable optical adhesive or the diffractive converging lens 201and the neutral filter 220 are coupled to one another optically by meansof a liquid having matching refractive index and held in this position.

It is clear that the neutral filter 220 can be combined with anydiffractive optical elements having varying structural heights, inparticular also with that in FIG. 3.

The diffractive structure can also be applied directly to the neutralfilter. For this purpose, the diffractive optical element and theneutral filter are made from one material. The diffractive opticalelement can then be structured in the neutral filter itself.

The neutral filter 220 has, in the region of the diffraction structure204, complete transparency, whereas it is completely opaque in theregion of the diffraction structure 209.

The total efficiency pattern of the optical arrangement comprising thediffractive converging lens 201 and the neutral filter 220 isillustrated in FIG. 13. In the latter, as in FIG. 7, the localdiffraction efficiency pattern of the diffractive converging lens 201 isshown as a full line. The local total efficiency pattern of the opticalarrangement comprising the diffractive converging lens 201 and theneutral filter 220 is shown in FIG. 13 as a chain-dot line. Proceedingfrom a value TO for the innermost diffraction structure 204 in FIG. 12,the total efficiency of the optical arrangement decreases to 0 towardsthe rim.

Of course, the diffractive converging lens 201 and the neutral filter220 may also be components that are spatially separated from oneanother.

Alternatively, the neutral filter may also be replaced by a metalcoating of the diffractive converging lens. Such metal coatings, whichhave a required transmission pattern, are known.

The efficiency considerations stated within the framework of thedescription of the figures may also be put forward analogously for areflective diffractive optical element. In this case, too, the samebasic dependencies of the diffraction efficiency on the structural widthor the structural height exist.

In the case of a reflective diffractive optical element, a reflectivecoating is normally used to optimize the reflection efficiency. In thisconnection, a metal coating or a dielectric, highly reflective (HR)coating may be used. The diffractive structure may be disposed in thislatter case on or under the HR layer system. The material of thediffractive structure may differ in both cases from the materials usedin the HR layer system. Particularly good efficiency results areobtained if the refractive index of the layer of the HR layer systemthat is immediately adjacent to the diffraction structures is chosen insuch a way that the inner periodicity of the HR layer system iscontinued by the layer that is required by the diffraction structures.In the case of an HR layer system having alternating high-refractivityand low-refractivity layers, the first layer of the HR layer system thatis immediately adjacent to the diffraction structures should, forexample, be highly refractive if the layer that is required by thediffraction structures is of low refractivity.

1. A diffractive optical element comprising a plurality of diffractionstructures each having a width, which is measured in a plane defined byan overall extension of the diffractive optical element, and a height,which is measured vertically to the plane, wherein wider diffractionsstructures have a lower height than less wide diffraction structuressuch that the wider diffraction structures have a larger diffractionefficiency than less wide diffraction structures.
 2. The diffractiveoptical element according to claim 1, wherein the heights of thediffraction structures are inversely proportional to their widths insuch a way that a local diffraction efficiency of the diffractiveoptical element is approximately constant across the diffractive opticalelement.
 3. The diffractive optical element according to claim 1,wherein the heights of the diffraction structures vary in such a waythat a local diffraction efficiency of the diffractive optical elementfollows a required diffraction efficiency function across thediffractive optical element.
 4. The diffractive optical elementaccording to claim 3, wherein the diffraction efficiency function is anapodization function.
 5. The diffractive optical element according toclaim 1, wherein the diffractive optical element includes a radius suchthat the diffraction structures are disposed coaxially and annularly,wherein the radially measured widths and the axially measured heightsvary over the radius of the diffractive optical element.
 6. Thediffractive optical element according to claim 1, further including acoating that increases the diffraction efficiency.
 7. The diffractiveoptical element according to claim 1, wherein the diffractive opticalelement is of a transmissive design.
 8. The diffractive optical elementaccording to claim 1, wherein the diffractive optical element is ofreflective design.
 9. A diffractive optical element comprising aplurality of diffraction structures each having a width, which ismeasured in a plane defined by an overall extension of the diffractiveoptical element, and a height, which is measured vertically to theplane, wherein wider diffractions structures have a lower height thanless wide diffraction structures such that a local diffractionefficiency of the diffractive optical element is a linear function of adistance of the diffraction structures from a central point of thediffractive optical element.
 10. A diffractive optical elementcomprising a plurality of diffraction structures each having a width,which is measured in a plane defined by an overall extension of thediffractive optical element, and a height, which is measured verticallyto the plane, wherein wider diffractions structures have a lower heightthan less wide diffraction structures, and wherein the widths of thediffraction structures increase monotonically from a central point ofthe diffractive optical element.
 11. A diffractive optical elementcomprising a plurality of diffraction structures each having a width,which is measured in a plane defined by an overall extension of thediffractive optical element, and a height, which is measured verticallyto the plane, wherein wider diffractions structures have a lower heightthan less wide diffraction structures, and wherein the widths of thediffraction structures vary as a function of a distance from a centralpoint of the diffraction optical element, the function having at leastone intermediary maximum or minimum.
 12. A diffractive optical elementcomprising a plurality of diffraction structures each having a width,which is measured in a plane defined by an overall extension of thediffractive optical element, and a height, which is measured verticallyto the plane, wherein wider diffractions structures have a lower heightthan less wide diffraction structures, and wherein variations of theheights of the diffraction structures are computed in such a way thatthe local diffraction efficiency follows a given diffraction efficiencyfunction that specifies for each diffraction structure a certain localdiffraction efficiency.